Assimilation de données pour la prédiction de paramètres hydrodynamiques et écologiques : cas de la lagune de l'Oder

Abstract : The management of ocean and coastal systems needs short term predictions of their physical and ecological state. The success of Data Assimilation (DA) in meteorology proves the ability to improve the forecast of a dynamical model by incorporating in-situ data.
This work focuses on sequential DA, derived from the theory of statistical estimation, and especially on the Kalman filter (KF). The difficulties of applying the KF in oceanography are twofold:

  • theoretical since the dynamical equations of physics and ecology are nonlinear while the KF is only optimal for linear systems,
  • practical because the high resolution discretization required for the accurate modeling of three-dimensional systems leads to state dimensions up to a million parameters, implying huge memory requirements and computational burden although efficiency is crucial for operational forecasting.

In the general case there is no solution that fits both requirements yet but classical approximations of the KF are used, either with a Taylor expansion (Extended Kalman filter EKF) or by Monte-Carlo approximation (Ensemble Kalman filter EnKF). Since all KF, EKF and EnKF use a linear estimation for the model update that is formally equivalent to a kriging with known mean, modifications inspired from geostatistics are proposed to account for bias or nonlinearities.
Two popular methods in oceanography, the RRSQRT KF (an approximation of the EKF by eigenvalue decomposition) and the EnKF, are compared in a twin experiment using a 1-D ecological model of a water column. The RRSQRT KF is then applied to DA of water levels in the 3-D hydrodynamical model TRIM3D of the Odra lagoon. The estimation is improved using the measurements of only three pile stations and intialization times are dramatically reduced. Last, the EnKF is applied to joint assimilation of water level (5 stations) and salinity (2 stations) in TRIM3D as a transport model for the Odra lagoon. Some difficulties in using sequential DA with advection-diffusion models are reported.
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Submitted on : Friday, July 16, 2004 - 12:19:48 PM
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  • HAL Id : tel-00005782, version 1

Citation

Laurent Bertino. Assimilation de données pour la prédiction de paramètres hydrodynamiques et écologiques : cas de la lagune de l'Oder. Mathématiques [math]. École Nationale Supérieure des Mines de Paris, 2001. Français. ⟨tel-00005782⟩

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